Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Dorin Andrica is a professor of mathematics at Babeş-Bolyai University in Cluj Napoca, Romania. His interests include Critical Point Theory and Applications, Nonlinear Analysis, Approximation Theory, Number Theory. Other than his several research publications, Prof. Andrica has published extensively with Springer on an array of topics. Being a master of Olympiad caliber problems, he has couched several teams for the Mathematical Olympiads and has published popular books in this subject.

Themistocles M. Rassias is a professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Prof. Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Prof. Rassias has published as author or editor many books and volumes with Springer. In addition to having received several awards, Themistocles M. Rassias’ work has received a large number of citations.

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